Description
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Friendly introduction to higher index theory, a growing subject at the intersection of geometry, topology and operator algebras.
About the Author
Rufus Willett is Professor of Mathematics at the University of Hawaii, Manoa. He has interdisciplinary research interests across large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras. Guoliang Yu is the Powell Chair in Mathematics and University Distinguished Professor at Texas A & M University. He was an invited speaker at the International Congress of Mathematicians in 2006, is a Fellow of the American Mathematical Society and a Simons Fellow in Mathematics. His research interests include large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras.
Reviews
'This book is an exceptional blend of clear, concise, delightfully written exposition and thorough scholarship. The book also has much to offer more experienced researchers.' Peter Haskell, European Mathematical Society
Book Information
ISBN 9781108491068
Author Rufus Willett
Format Hardback
Page Count 592
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 940g
Dimensions(mm) 234mm * 158mm * 36mm
Friendly introduction to higher index theory, a growing subject at the intersection of geometry, topology and operator algebras.
About the Author
Rufus Willett is Professor of Mathematics at the University of Hawaii, Manoa. He has interdisciplinary research interests across large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras. Guoliang Yu is the Powell Chair in Mathematics and University Distinguished Professor at Texas A & M University. He was an invited speaker at the International Congress of Mathematicians in 2006, is a Fellow of the American Mathematical Society and a Simons Fellow in Mathematics. His research interests include large-scale geometry, K-theory, index theory, manifold topology and geometry, and operator algebras.
Reviews
'This book is an exceptional blend of clear, concise, delightfully written exposition and thorough scholarship. The book also has much to offer more experienced researchers.' Peter Haskell, European Mathematical Society
Book Information
ISBN 9781108491068
Author Rufus Willett
Format Hardback
Page Count 592
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 940g
Dimensions(mm) 234mm * 158mm * 36mm
